A further study of P-wave attenuation across parallel fractures with linear deformational behaviour

When a wave propagates through fractured rock masses, it is greatly attenuated (and slowed) due to the presence of fractures. In the situation where dynamic responses are induced by a far field explosion or vibration, the magnitude of the stress wave is generally too small to mobilize nonlinear deformation of the fractures, so linear deformational behaviour is adopted in studying wave attenuation. Cai and Zhao [Effects of multiple parallel fractures on apparent wave attenuation in rock masses. Int J Rock Mech Min Sci 2000;37(4): 661–82.] used the method of characteristics to study P-wave attenuation across linear deformational fractures by considering interfracture wave reflections. However, the frequency characteristic of the incident wave (a one-cycle sinusoidal wave) was overlooked in their previous study. The present study treats the incident wave as the sum of a series of harmonic waves in the frequency domain. Results and wave phenomena in the previous study are improved and better understood. When the incident wavelength is substantially greater than fracture spacing, an equivalent medium method is developed to explain the wave phenomena in such a situation. In addition, the uncertainty of back analyzing fractured structures and the effects of wave frequency are examined. These results are in accordance with conclusions in the field of geophysics.